Question

A genetics experiment involves a population of fruit flies consisting of 2 males named Bart and Carlos and 2 females named Diana and Elaine. Assume that two fruit flies are randomly selected with replacement.After listing the possible samples and finding the proportion of males in each sample, use a table to describe the sampling distribution of the proportion of males.
Proportion of males Probability
0 [ ]
0.5 [ ]
1 [ ]

Answer 1

Answer:

$\begin{equation*} \begin{matrix}Proportion of males & Probability \\0 & \frac{9}{16} \\0.5 & \frac{3}{8} \\1 & \frac{1}{16} \end{matrix} \end{equation*}$

Step-by-step explanation:

The sample space consists of

1 male named Bart (b)

3 females named Charlene(c), Diana(d), and Erin(e).

Since there is replacement, the possible samples are:

bb, bc, be, bd, cb, cc, cd, ce, db, dc, dd, de, eb, ec, ed, and ee.

The total Number of pairs = 16

Event of picking 2 males: bb

Event of picking 1 male: bc,cb,bd,db,be,eb

Event of picking No male: cc, cd, ce, dc, dd, de, ec, ed, and ee.

Proportion of 0

P(No Male)=$\frac{9}{16}$

Proportion of 0.5

P(1 male out of 2)=$\frac{6}{16}=\frac{3}{8}$

Proportion of 1

P(2 male out of 2)=$\frac{1}{16}$

$\begin{equation*} \begin{matrix}Proportion of males & Probability \\0 & \frac{9}{16} \\0.5 & \frac{3}{8} \\1 & \frac{1}{16} \end{matrix} \end{equation*}$